Finite Group DatabasebetaFinite Group DatabasebetaOrder 432.
198 conjugacy classes of subgroups; only the 68 normal subgroups are shown.
This group has 198 conjugacy classes of subgroups — too many to draw. Only its 68 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C32×Dic6 | C2 | semidirect |
| 3. C3×#627 | C2 | semidirect |
| 6. #3797 | C3 | direct (N × H) |
| 18. C3×Dic6 | D3 | semidirect |
| 19. C3×Dic6 | C2×C3 | semidirect |
| 20. #627 | C2×C3 | semidirect |
| 23. C3×C3⋊D3 | Q8 | semidirect |
| 41. C33 | C2×Q8 | semidirect |
| 52. Dic6 | C3×D3 | semidirect |
| 58. C3⋊D3 | C3×Q8 | semidirect |
| 80. C32 | D3×Q8 | semidirect |
| 81. C32 | C2×C3×Q8 | semidirect |
| 101. C3 | #3797 | direct (N × H) |
| 102. C3 | C3×D3×Q8 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×C4×C3⋊D3 | 2 |
| C32×Dic6 | 2 |
| C3×#627 | 2 |
| C3×#624 | 2 |
| C3×D3×Q8 | 3 |
| #3797 | 3 |